通过机器学习回归不确定性揭示自驱动活性粒子的聚集相变
Reveal flocking phase transition of self-propelled active particles by machine learning regression uncertainty
AI总结：
本研究提出基于神经网络的“回归不确定性学习”方法，以Vicsek模型的自驱动活性粒子聚集相变为对象，利用回归不确定性的M形曲线谷值定位相变临界点，该方法相比传统分类学习方法更具通用性与物理解释潜力。
摘要：
我们开发了基于神经网络的“从回归不确定性中学习”方法，用于自动检测非平衡活性系统中的物质相。以Vicsek模型描述的自驱动活性粒子的聚集相变为例，我们发现：在训练神经网络解决逆统计问题（即执行从这类非平衡多体复杂系统的稳态构型样本中重建噪声水平的回归任务）后，训练良好的网络得到的回归结果不确定性实际上可用于揭示所研究系统中可能存在的相变。回归不确定性的噪声水平依赖关系呈现出非平凡的M形，其谷值出现在聚集相变的临界点处。通过将这种基于回归的方法与广泛使用的基于分类的“混淆学习”和“空白学习”方法直接比较，我们表明我们的方法具有实际有效性、高效性，对跨学科领域的各种物理系统具有良好的通用性，并且更有可能通过传统物理学概念进行解释。这些方法可以相互补充，作为一个有前景的通用工具箱，用于研究丰富的临界现象，并为各种相变的存在提供数据驱动的证据，特别是对于那些与一级相变或非平衡活性系统相关的、传统物理学研究方法可能面临困难的复杂场景。
英文摘要：
We develop the neural network based "learning from regression uncertainty" approach for automated detection of phases of matter in nonequilibrium active systems. Taking the flocking phase transition of self-propelled active particles described by the Vicsek model for example, we find that after training a neural network for solving the inverse statistical problem, i.e., for performing the regression task of reconstructing the noise level from given samples of such a nonequilibrium many-body complex system's steady state configurations, the uncertainty of regression results obtained by the well-trained network can actually be utilized to reveal possible phase transitions in the system under study. The noise level dependence of regression uncertainty assumes a non-trivial M-shape, and its valley appears at the critical point of the flocking phase transition. By directly comparing this regression-based approach with the widely-used classification-based "learning by confusion" and "learning with blanking" approaches, we show that our approach has practical effectiveness, efficiency, good generality for various physical systems across interdisciplinary fields, and a greater possibility of being interpretable via conventional notions of physics. These approaches can complement each other to serve as a promising generic toolbox for investigating rich critical phenomena and providing data-driven evidence on the existence of various phase transitions, especially for those complex scenarios associated with first-order phase transitions or nonequilibrium active systems where traditional research methods in physics could face difficulties.
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